# I Eigenspectra and Empirical Orthogonal Functions

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1. Apr 8, 2016

### ecastro

Are the Eigenspectra (a spectrum of eigenvalues) and the Empirical Orthogonal Functions (EOFs) the same?

I have known that both can be calculated through the Singular Value Decomposition (SVD) method.

2. Apr 13, 2016

### Greg Bernhardt

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. May 2, 2016

### akeleti8

Hi there. Eigenspectra is a spuctrum of eigenvalues. eigenvalues are values of a scalar so that [PLAIN]https://upload.wikimedia.org/math/3/6/4/364442fc3d24dc6d566c98cfa307b1f0.pngx=Bx. [Broken] B is any given function. The eigenvalues of a matrix J can be found by finding det( J - [PLAIN]https://upload.wikimedia.org/math/3/6/4/364442fc3d24dc6d566c98cfa307b1f0.pngI). [Broken] empirical orthogonal functions are a means of decomposing a dataset in terms of orthogonal basis functions. This is not what eigenspectra are.

This is a congenial problem for development for an anorthosite loving kid. i use wolfram alpha to help me with this problem. .

Last edited by a moderator: May 7, 2017
4. May 3, 2016

### ecastro

From an article I have been reading, the eigenspectra they discuss can be calculated from a collection of data. They then use these eigenspectra to reconstruct some parts of the data.

$E = a_1 \hat{e}_1 + a_2 \hat{e}_2 + a_3 \hat{e}_3 + \cdots$,

where $E$ is the reconstructed signal, $a_1, a_2, a_3, ...$ are coefficients, and $\hat{e}_1, \hat{e}_2, \hat{e}_3, ...$ are what they call the eigenspectra. Isn't this also how the Empirical Orthogonal Functions are used to reconstruct a signal or data?

5. May 23, 2016

### Stephen Tashi

Is the article available online ? What's the article about ?

6. May 30, 2016

### ecastro

The article's title is "Accuracy of Spectrum Estimate in Flourescence Spectral Microscopy with Spectral Filters". The article is about the reconstruction of a sample's spectrum.